Time series behaviour of inflation

We investigate changes in the time series properties of inflation prior to the inflation targeting monetary and after its adoption. From the summary statistics reported in Table 6.1, the mean/average of the pre-IT inflation is almost twice of the mean of the post-IT inflation. The pre-IT mean inflation is about 178 % more volatile than the post-IT period. It suggests that inflation has generally reduced after the adoption of the IT regime. Also, the range (defined as the difference between the maximum and minimum inflation rates) is less in the post-IT (3.59) compared to the pre-IT rates (8.48). The standard deviation is also less for the post-IT period. We observe that the skewness for the period before IT indicates some asymmetry around the mean, whereas the kurtosis points to some peakedness relative to the normal. These suggest some deviation from the normality assumption as indicated by the large statistics for the Jarque- Bera (JB) in both the full sample and the pre sample.

The JB test for normality, however, indicates that the period after the IT has a normal distribution unlike the pre-IT period. The pre-IT series is slightly leptokurtic. The figures suggest that there is a significant volatile behaviour of month-on-month inflation in Ghana, both before and after the inflation targeting, however slightly less volatile in the post-IT period. The number of observations in the post targeting sample is only 38 % of the number of observations in the pre sample. Figure 6.1 contains graphs of the inflation in Ghana for the period 1990 to 2013 and two separate graphs for the pre-inflation targeting and post-inflation targeting regime.

Table 6.1: Summary statistics for inflation Statistic 1990M1 – 2013M12 1990M1 – 2007M5 2007M6 – 2013M12 Ratio ()31 Mean 1.50 1.71 0.96 1.78 Median 1.38 1.50 1.15 1.30 Maximum 12.04 12.04 5.14 2.34 Minimum -3.56 -3.56 -1.56 2.28 Std. Dev. 1.63 1.72 1.26 1.37 Skewness 1.28 1.37 0.01 137 Kurtosis 9.10 9.12 3.46 2.64 Jarque-Bera 524.93** [0.00] 391.10** [0.00] 0.69 [0.70] N/A Observations 287 208 78 2.67

Note: ** indicate rejection at the 5% significance level

31 _{Following Hudson and Mosley (2008), we divide the statistics for the before and after periods as a measure of relative}

Figure 6.1: Graphical representation of inflation (1990M1 - 2013M12)

Pre-IT inflation (1990M1 - 2007M5)

Post-IT inflation (2007M6 – 2013M12)

We consider the long memory and persistent behaviour of inflation by using unit root and fractional integration techniques. Coleman (2012) assesses the impacts of regional and sectoral inflation persistence and provides findings of asymmetries in inflation persistence in Ghana. The evidence suggested that some regions and sectors are more likely to feel the impact of inflationary shocks than others, and the attendant welfare losses are likely to be high for those regions and sectors with high inflation persistence. Alagidede et al. (2014) updates the study to cover up to the first quarter of 2014 and provides similar evidence.

We employ their approach to measure the properties of the inflation series for the pre and post inflation targeting periods. The Geweke and Porter-Hudak (GPH, 1983) approach estimate of the fractional differencing estimator, d, is based on a regression of the ordinates of the log spectral density on trigonometric function. The technique makes use of nonparametric spectral regression model to estimate d without categorical specification of the ―short memory‖ or ARMA parameters. In order for the d estimate to fall within the range [-0.5, to 0.5] interval, the series is usually differenced.

The modified log periodogram regression estimator which was proposed by Phillips (1999a, 1999b), is a modified form of the GPH. The approach addresses a weakness of the GPH estimator and estimates the d by modifying the dependent variable to return the distribution of d under the null hypothesis that d=1 and the estimator gives rise to a test statistic for d=1. Given that the GPH estimator may be problematic against d>1 alternatives where d exhibits asymptotic bias toward unity, Phillips‘ approach distinguishes unit-root behaviour from fractional integration. This test is more efficient against both d>1 and d<1 options.

The unit root results presented in Table 6.2 contains results for unit root tests and estimates of fractional integration parameter. The results indicate that the series are I(0), as the null

hypothesis of I(1) is rejected except for few instances. The ADF test fails to reject the null of I(1) for the post-IT inflation series. In the case of the long memory estimations, the two methods give the same estimate for the pre-IT series whereas a marked difference exists in the estimates for the post-IT period. The GPH estimate is almost half of the other estimate. However, based on the unit root, it can be concluded that the series are I(0) in general. These tests fail to distinguish series that are 0 < d < 1.

The GPH and modified log periodogram tests provide evidence of long memory and persistence in the series. The presence of stationary long memory portrays autocorrelations that take far longer to decay than the exponential rate associated with ―short memory‖ processes. Thus, the series cannot be classified as either I(0) nor I(1) process; but rather an I(d) process. The implication of this finding is that the data generating processes of inflation are associated with persistence and may be predictable at long horizons.

Table 6.2: Tests of integration

Test 1990M1 – 2013M12 1990M1 – 2007M5 2007M6 – 2013M12 ADF1 -8.07 (0) -6.93 (0) -1.20 (1) ADF2 -8.34 (0) -6.98 (0) 0.42 (1) PP1 -7.89 (0) -7.01 (0) -4.42 (0) PP2 -7.93 (0) -7.08 (0) -4.41 (0) KPSS1 0.83 (1) 0.35 (0) 0.13 (0) KPSS2 0.07(0) 0.10 (0) 0.04 (0) GPH 0.33** [0.00] 0.50** [0.00] 0.32** [0.00] Modified LogPeriodogram 0.51** [0.00] 0.50** [0.00] 0.61** [0.00]

Notes: The subscript 1 represent tests with constant only whilst the subscript 2 indicates tests with both constant and trend. The ADF and PP tests have H0 of unit root whereas the KPSS has H0 of stationary series. Whereas the unit root and stationary tests distinguish between I(0) and I(1) processes, the long memory tests reports the d as a real number. For ADF and PP, the null of unit root is rejected if the statistics is less than the critical values. For KPSS, the null of stationary series is not rejected if the statistics is smaller than the criticalvalues. Values in ( ) are the levels of integration, I(0) or I(1). For the long memory tests, the values in parenthesis are p-values and ** indicate significance at 5% level.