5.1. Cointegration Test
The ADF test would imply that each price series shown in
Table 2 contains unit roots which are a condition for cointegration. The ADF test requires many steps in order to conclude that the data series is non-stationary. The AIC suggests the selection of one lag for each series. All the data series were found likely to be integrated to the order of one I(1). To ascertain this, the last test required testing a null hypothesis of the I(2) price series against the alternative hypothesis of a I(1) price series. The tau statistic concluded that the null hypothesis was rejected and the alternative hypothesis was accepted.
As the price series in the analysis were found to contain unit roots, the aim of this paper was, therefore, to test whether the price series are cointegrated for two dairy products (fresh milk and powdered milk) based on their geographical location. The urban areas were Lilongwe, Blantyre, Zomba and Mzuzu, with Mzuzu being the northern city of interest. The Johansen cointegration procedure was used as this allows some inference on the number of cointegrating relationships within the data.
The Johansen cointegration test results (
Table 3) found it likely that four cointegrating vectors existed at 1% statistical significance level. This does provide evidence to suggest that there is a likely cointegrating relationship for the products with regards to their respective four markets (i.e., Lilongwe, Blantyre, Zomba and Mzuzu). This result helps to support the idea of the law of one price being applicable, at least in the long run to these products in the different locations. However, it should be noted that the informal sectors of dairy marketing cannot be covered in this paper owing to data constraints. The estimation of the cointegration of fresh milk raised a warning message and the test could not estimate the test statistic for the first null hypothesis, since there were zero vectors of cointegration. However, it seems very likely given the other null hypothesis results that the test statistic should allow the rejection of the null hypothesis.
Pairwise cointegration tests were run with regards to Mzuzu and are shown in
Table A1,
Table A2 and
Table A3 within
Appendix A. With regards to fresh milk, results suggest that cointegration exists between Mzuzu and Blantyre but not for the other pairings. This result does suggest that pairings of either Lilongwe or Zomba to Mzuzu do not experience the law of one price in the long run, hence the focus should be on the Mzuzu to Blantyre pairing. With regards to powdered milk, it is likely that all pairings have a cointegrating vector.
The cointegration results would imply that, in the long run, the theory of the law of one price holds (at least for the Mzuzu to Blantyre pairing), which suggests that retailers price dairy products at a similar level. However, the deviations from this level in the short term are where the threshold models are of particular interest hence the focus of this paper on spatial market integration.
5.2. Threshold Vector Autoregressive and Vector Error Correction Models
In order to account for transaction costs, both a threshold vector autoregressive model (TVAR) and threshold vector error correction model (TVECM) are used.
The urban threshold pairs concern how the flow of dairy products go to the northern town of Mzuzu, hence all pairings start with Mzuzu. In
Goodwin and Piggott (
2001)’s paper the focus was on the main market trading town of Williamston for corn hence this town was the last pairing as corn was being delivered there. The larger thresholds equate to larger transaction costs (
Goodwin and Piggott 2001). Since Mzuzu is unlikely to be an exporter of dairy products it would not make sense to have it as the last pairing. One problem with the data range used is that the most recent period was April 2011, which covers a time during which Northern Dairies Industries was still in operation and this may have distorted the results. However, it seems unlikely that Northern Dairies Industries was an efficient processor since it closed in 2012.
Table 4 and
Table 5 show the TVAR and TVECM modelling results.
The threshold values of urban fresh milk
2 (
Table 4) reveal that the largest gap between threshold values
3 is for the pairing Mzuzu–Lilongwe. However, in terms of where the majority of observations occur, the TVAR and TVECM have similar results. The relatively large thresholds may be a result of transportation costs. With regards to the frequency of observations for the pairing of Mzuzu–Lilongwe, the results suggested that the majority of observations are in the middle regime (i.e., regime 2) which is likely to be a result of the towns being close to one another hence possible market integration. This highlights that the thresholds should be covered alone. The TVECM frequency observation results would suggest that deviations from the equilibrium are not usually large enough to exceed regime 2.
There was a similar result for the pairing of Cofield and Williamston in the study by
Goodwin and Piggott (
2001) in which the regions were close in terms of distance and had a majority of observations in regime 2.
The Mzuzu–Blantyre pairing is where the two models return somewhat different results. The TVAR indicated that the majority of observations were within regime 2, which is in contrast to the TVECM which indicates regime 1. As the TVAR model is assumed to be symmetric, this may have overestimated the number of observations occurring in the neutral band.
If more data were available, then a more seasonal understanding could be formed as there is low output of fresh milk produced in the dairies of Lilongwe. In 2011, Lilongwe took deliveries of approximately 9.7% of total raw milk (from Malawian milk bulking groups) with the remaining share going to dairies based in the south of the country (including Blantyre) (
Revoredo-Giha et al. 2013). This would imply that a relatively small volume of milk is produced in Lilongwe and there may be little available for Mzuzu, thus the transaction costs are higher for Blantyre’s fresh milk products (this may support the lack of cointegration vectors in the Mzuzu to Lilongwe pairing). It must be emphasized that MDI (from which the data were sourced) is the smaller dairy in Lilongwe.
With regards to powered milk, it seems that the lowest thresholds (i.e., transaction costs) found in both the TVAR and TVECM are for Mzuzu to Lilongwe. Also, both models found that the majority of observations were in regime 2, which implies greater market integration (
Greb et al. 2013). This result seems credible since the distance is shortest and powdered milk does not require refrigeration vehicles. A recent survey suggests that powdered milk represents the largest share of weekly consumed dairy products and is often imported (
Revoredo-Giha and Akaichi 2013).
Due to the dominance of powdered milk in the sampled Malawian diet this is an important result since transaction costs are lowest for this pairing, which suggests that the market is working efficiently. There is also the possibility that as powdered milk can be stored without refrigeration facilities, warehouses in Lilongwe are able to store the products, thus involving lower transaction costs. The distance to the northern towns would support this finding that a greater distance results in greater transaction costs.
The TVECM results for the other pairings differed to the TVAR. While the TVAR reported that the majority observations were in regime 2, the TVECM found that, for both pairings, they were either in regime 1 or 3. A possible explanation for the TVECM result is that should Lilongwe be unable to provide powdered milk, then Blantyre must provide the powdered milk which
Greb et al. (
2013) explained distorts the spatial equilibrium, thus resulting in price transmission. This could possibly result in a positive price transmission, although more data would be required in order to support this hypothesis. However, both models conveyed a similar finding that the thresholds were larger for the Mzuzu–Blantyre, or the Mzuzu–Zomba pairing, relative to the Mzuzu–Lilongwe pairing.
Whilst some of these findings are similar to
Goodwin and Piggott (
2001)’s finding that greater distances result in higher transaction costs, there are some differences in terms of the modelling. The TVAR model used in this study offered basic results and would have been improved if a Tsay’s test were available such as in the case of
Goodwin and Piggott 2001 although
Abdulai (
2000)’s study did not use this test. The general finding that transaction costs are higher based on larger distances is supported by the findings of
Mtumbuka et al. (
2014) who found a similar situation occurring for the Malawian bean market.