Six markets and above under rule of one price

When log of transaction cost is assumed to be constant with out any control on seasonal effect and assuming un0trended level data under vector error correction model with restrict constant, it is not possible to find any market combination with one common trend; given the error vectors are white noise.

And even using vector error correction model with restricted trend which allows not only for possibility of trended log of transaction cost and deterministic trend in level data but also capacity to control seasonality by using centered seasonal dummy it is not possible to find six markets which are sharing one common trend at any possible lag. And for both restricted constant and restricted trend model six markets under rule of one price can’t be found, even if the less restrictive distributional assumptions are maintained in which than error term level normality vector level normality and than independence at each serial lag, vector level independence at cumulative serial lag are demanded.

However when unrestricted constant is used assuming constant log of transaction cost and trended level data, which allows for controlling seasonal variation, it was possible to find three combinations of six markets cointegrated under rule of one price, with out restriction on lag used. These three combinations are discussed below.

3.8.1. Unrestricted constant model

Table 59, below, clearly show that based on both trace statistics and Maximum Eigen value the null of 0 to 4 cointegration equations are rejected with 99% confidence but the null of one common trend or the null that these combination of markets are governed by rule of one price can’t be rejected at 5% level.

Table 59 for model with constant rank test for six markets

MARKET critical values statistics Rank G0S0N0B0J0D S0G0A0N0J0M G0M0S0A0D0J 5% 1% 0 784.533 307.1224 536.5821 94.15 103.18 1 406.6542 181.5819 265.1458 68.52 76.07 2 226.6403 114.6545 168.9862 47.21 54.46 3 102.4121 68.6518 87.2803 29.68 35.65 4 25.3338 29.2184 25.9391 15.41 20.04 Trace statistics 5 1.2725 0.001 0.3885 3.76 6.65 0 377.8788 125.5405 271.4363 39.37 45.1 1 180.0139 66.9274 96.1596 33.46 38.77 2 124.2283 46.0027 81.7059 27.07 32.24 3 _{77.0783 39.4334 61.3412 20.97 25.52} 4 _{24.0613 29.2174 25.5507 14.07 18.63} Maximum Eigen value 5 1.2725 0.001 0.3885 3.76 6.65

So assuming that the lags used are appropriate it could imply that there is strong cointegration under rule of one price between these three combinations of six markets given in table 59, above. Given the fact that rank test is based on correct specification of the cointegration equation, the million dollar question is ‘are the model used having an appropriate specification?’

In all three combinations the null of independently distributed error vectors can’t be rejected up to 57% level (see table 60, below). Given the fact that these three combinations are selected to represent strongly cointegrated marketed by demanding that the null of independently distributed error vector not to be rejected at 10% level, on all serial lags from 1st to 15th , it is logical to conclude that there is no evidence of any serial correlation in all error vectors. The null of normality is also not rejected even at 64% for all combinations and given for each error term the null of normality is not rejected at 10% level the implication is that the error vectors are strongly normally and independently distributed as demanded by rank test.

Table 60 for model with restricted trend lag, normality and serial correlation testes for six markets

likelihood–ratio based lag

selection Normality test

Serial correlation test Markets Lag

used

FPE AIC HQIC SBIC Statistic

(12 – df) Prob Statistic (5400df) Prob G0S0N0B0J0D 11 1 1 1 1 4.2 0.979 532. 9 0.578 S0G0A0N0J0M 10 1 6 1 1 9.6 0.65 522.2 0.701 G0M0S0A0D0J 11 1 1 1 1 3.9 0.985 531.5 0.595

However the lag fitted is found to be much larger than the lag selected by all information criterions. Under such over fitted cointegration vectors Monte Carlo evidence did show that rank test have tendency to find cointegration when there is no real cointegration. So it is logical to conclude that there are no six markets which are following one strong common trend or strongly governed by rule of one price. And even if relaxed assumptions are demanded on the distribution of the error vectors it is not possible to find six markets under rule of one price.

3.8.2. More than six markets under rule of one price

Even if 7 and 8 markets are considered it was not possible to find markets under rule of one price for both restricted distributional requirement and relaxed distributional requirements and all models. So in general which ever model is used it is not possible to find six or more markets which are sharing one common trend or which are governed by rule of one price. The logical conclusion that could follow will be that the whole country is not ruled by one price but there are two combinations of five markets which are sharing two different single common trends. How ever analysis in common trend below will show that both combinations are sharing the same common trend. The reason the combinations are not cointegrating in to one common trend based on rank test is because their error vectors was found to be highly none white noise at first lag. This is clear evidence that rank test which is developed for varibles with white noise errors may be is inadequate in all cases. More over the search procedure followed by Gonz´alez0Rivera

and Helfand (2001) will not fail to find the strongly cointegrated markets under rule of one price, if information on common trend given below is considered. But if analysis for Ethiopian wheat markets was based only on rank test, only, it will end up in inconclusive result. Even though their methodology is convenient for application, it is not theoretically sound. Fortunately for Ethiopian data used there would be no difference on conclusion, if their methodology or the more tedious search for all possible permutations, as done in this paper is used. How ever distributional assumptions have to be tested at each stage even in their methodology.

Unfortunately the use of distance in order of inclusion recommended by Gonz´alez0 Rivera and Helfand (2001) and used by Rashid (2006) is not sound in under developed market economy like Ethiopia with high market failures and dysfunctional institutions. And this is clearly seen in the above analysis. Coming to Ethiopian wheat market before possible recommendations are given, let’s try to grasp the full picture by estimating the common trend and the short run dynamics of the markets.