Russian Journal of Agricultural and Socio-Economic Sciences ...

H. DE-GRAFT ACQUAH, University of Cape CoastWhere 7 is the Heavside indicator, ; thenumber of lags, 3 3 and the coefficients and :the threshold value. The lag ; is specified to accountfor serially correlated residuals and it canbe calculated using Bayesian Information Criteria(BIC) or Akaike Information Criteria (AIC).The threshold value :can be specified as zero.Alternatively, Chan (1993) proposes a searchmethod for obtaining a consistent estimate of thethreshold value. A super consistent estimate ofthe threshold value can be attained with severalsteps. First, the process involves sorting in ascendingorder the threshold variable, i.e. forthe threshold model. Second, the possible thresholdvalues are determined. If the threshold valueis to be meaningful, the threshold variablemust actually cross the threshold value. Thus, thethreshold value : should lie between the maximumand minimum values of the threshold variable.In practice, the highest and lowest 15% ofthe values are excluded from the search to ensurean adequate number of observations on each side.The middle 70% values of the sorted thresholdvariable are used as potential threshold values.Third, the threshold model is estimated with eachpotential threshold value. The sum of squarederrors for each trial can be calculated and the relationshipbetween the sum of squared errors andthe threshold value can be examined. Finally, thethreshold value that minimizes the sum ofsquared errors is deemed to be the consistent estimateof the threshold. Against this background,two competing models are considered namely theThreshold model with : = 0 (i.e. TAR) and theconsistent threshold model with : estimated.Given the alternative models, model selectionprocedures such as the Akaike Information Criterion(AIC) and Bayesian Information Criterion(BIC) provides a basis for choosing between theThreshold Model (TAR) and Consistent ThresholdModel (CTAR). A model with the lowestAIC and BIC should be preferred.Insights into the asymmetric adjustments inthe context of a long run cointegration relationcan be obtained with two tests. First, an F-test isemployed to examine the null hypothesis of nocointegration (H 0 : 1 = 2 = 0) against the alternativeof cointegration with either TAR or ConsistentTAR threshold adjustment. The test statisticis represented by F. This test does not follow astandard distribution and the critical values inEnders and Siklos (2001) should be used. Thesecond one is a standard F-test to evaluate thenull hypothesis of symmetric adjustment in thelong-term equilibrium(H 0 : 1 = 2 ). Rejection ofthe null hypothesis indicates the existence of anasymmetric adjustment process.Data. This study employs weekly retail andwholesale prices for maize from January 1994 toDecember 2003 from Kumasi in the Ashanti Regionof Ghana. The weekly data for all prices areGhana cedi per 100kg and given the high level ofinflation in the period covered, prices are deflatedusing consumer price index (CPI) deflator. Thedata was obtained from the Ministry of Food andAgriculture in Ghana.RESULTS AND DISCUSSIONUnit root test. To determine the datageneratingproperties of the individual data, theKwiatkowski, Phillips, Schmidt and Shin (KPSS)test for stationarity (Kwiatkowski, et al., 1992)was performed. The results of the KPSS test inTable 1 show that the retail and wholesale pricesare non stationary and integrated of the order one.n/nWholesale(Levels)Wholesale(FirstDifference)Retail(levels)Retail (FirstDifference)Table 1 – KPSS unit root testTeststatisticsSource: Author’s calculationCritical values10 % 5 % 2.5% 1%0.2755 0.119 0.146 0.176 0.2160.017 0.119 0.146 0.176 0.2160.3839 0.119 0.146 0.176 0.2160.0151 0.119 0.146 0.176 0.216Threshold cointegration analysis. Thenonlinear cointegration analysis is conducted usingthe Threshold Autoregression models. TheTAR and Consistent TAR models are estimatedand the results are reported in Table 2. In selectingan appropriate lag to address possible serialcorrection in the residual series, a maximum lagof 12 is specified and tried at the beginning. Diagnosticanalyses on the residuals through AICand BIC all reveal that a lag of 2 is sufficient. Inestimating the threshold values for consistentTAR, the method by Chan (1993) is followed.The lowest sum of squared errors for the consistentTAR model is 1191.69 at the threshold valueof -2.554. Alternatively, the threshold value for23