Nonlinearity in Inflation A Case of Pakistan


Abstract Recent research work has shown that inflation rate is asymmetric and it is also well known that asymmetry is a non-linear phenomenon. In order to better understand this non-linearity in inflation of Pakistan, we investigate the possible presence of Smooth Transition Autoregressive (STAR) non-linearity in inflation series. The study finds that month on month inflation series for Pakistan possesses both logistic and exponential STAR type non-linearity. Exponential Smooth transition function was proven to be more relevant on the basis of Dijk et al. (2000). Therefore, we develop ESTAR model in this paper which outperforms its linear rivals in forecasting.


We usually develop models for forecasting purposes which we use in setting monetary and fiscal policies. Unfortunately, if we look into the history, the forecasting record of economic variables is poor. To some extent this could be owing to random human behaviour or availability of virgin data however rigid structural assumptions of the model may also be responsible for the weak forecasting performance (Moshiri, 1997). For instance if we try to estimate a model with a linear regression whose underlying data generating process (DGP) has a non-linear pattern will generate poor results. In this scenario only non-linear models will likely give better results. Stock and Watson’s (1999) prove that simple auto-regressive models, AR (p), out- perform other models, however, AR (p) models have low forecasting power if DGP is nonlinear (Dijk et al., 2000).

Recent empirical literature shows that the dynamic generating mechanism of inflation rate is asymmetric, i.e. its behaviour is different during different phases of business cycle. This means there is a possibility that inflation has a nonlinear data generating process. For example, Shyh- Wei Chen (2010) provides evidence of non-linearity of inflation rate in OECD countries. Similarly Yildirim (2004) in his thesis provides the evidence for non-linearity in Turkish inflation rate and estimates Logistic smooth transition auto-regressive model (LSTAR). Testing and modeling non-linearity in inflation rate has attracted substantial interest because they outperform their linear rivals in forecasting and also proven presence of non- linearity questions many different theories. In the presence of non-linearity in inflation, different theories will have to be re-evaluated for example fisher effect or quantity theory of money etc.

If inflation rate is non-linear then traditional unit root tests for stationarity will not work. This implies need to re-test unit root in inflation to estimate co-integration relationship with other macro-economic variables.

Despite the abundance of studies on the behavior of inflation rates in Pakistan, non-linearity has not been considered yet by the existing literature. This study is an attempt to bridge this gap. In order to test the hypothesis of non-linearity, we split annual real GDP growth ranges from 1950 to 2011 into two groups- above and below average growth. Then we try to explore the corresponding inflation rates responses to one standard deviation (SD) of GDP growth in both groups. We observe that one SD above the average brings a change of only 2 basis points while the change is 36 basis points for the below average group, which to some extent support our concept of asymmetry (non-linearity). After establishing this preliminary evidence of non-linearity in inflation we formally test and model the non-linearity phenomenon using the STAR model developed specially to address this issue.

In recent times a number of nonlinear models have been proposed to capture observed asymmetries. Comprehensive surveys are given by Granger and Teräsvirta (1993), Potter (1999) and Dijk et al. (2000). The most common nonlinear models are Threshold autoregressive (TAR) models smooth transition autoregressive (STAR) models and Markov-switching regime...

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