Analyzing South Africa’s inflation persistence using an ARFIMA model with Markov-switching fractional differencing parameter

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The successful conduct of monetary policy relies on accurately characterising inflation’s data generating properties. Monetary policy errors that allow inflation to transition to a high inflation regime that is very persistent might have costly economic implications as the central bank attempts to bring inflation to a lower regime, say at some target level. This paper studies the duration of inflation persistence over time and across various policy regimes. We test the inertial properties of South African inflation in a Markov-Switching autoregressive fractionally integrated moving average model. We isolate period of high inflation and low inflation and analyse how persistent it is. This is an unique application to South Africa. The use of a fractional differencing ARIMA model allows for the possibility that inflation is close to a unit root, however, still mean reverting. This implies that shocks to inflation is very persistent and take long to dissipate. The inflation persistence is measured using a test by Ng and Perron (2001). We show that inflation is more persistent during high inflation episodes relative to low inflation episodes and more volatile during low inflation periods compared to high inflation periods. We estimate that it takes approximately 70 months for 50 percent of the shocks to dissipate in a high inflation regime compared to 10 months in a low inflation regime. The model identifies three structural breaks - a low inflation regime from 1920 until 1960, a high inflation regime from 1961 until 2003, and another low inflation regime over part of the inflation targeting period, 2003-2014. We also show that inflation persistence in the high inflation regime transitioned to a low inflation regime only much later than the implementation of inflation targeting - hinting that agents take time to adjust expectations. This has an important consequence for monetary policy - monetary policy errors that allow inflation to transition to a high inflation regime may take many months for any corrective policy to become effective.